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LSSC
2001
Springer

A Quasi-Monte Carlo Method for Integration with Improved Convergence

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A Quasi-Monte Carlo Method for Integration with Improved Convergence
Abstract. Quasi-Monte Carlo methods are based on the idea that random Monte Carlo techniques can often be improved by replacing the underlying source of random numbers with a more uniformly distributed deterministic sequence. Quasi-Monte Carlo methods often include standard approaches of variance reduction, although such techniques do not necessarily directly translate. In this paper we present a quasi-Monte Carlo method for integration that combines a separation of the domain into uniformly small subdomains with the approach of importance sampling. Theoretical estimates for the error bounds and the convergence rate are established. A large number of numerical tests of the proposed method are presented and compared with crude Monte Carlo and weighted uniform sampling. All methods are realized using pseudorandom numbers, and Sobol, Halton and Faure quasirandom sequences. The numerical results confirm the improved convergence of the proposed method when the integrand has bounded derivat...
Aneta Karaivanova, Ivan Dimov, Sofiya Ivanovska
Added 30 Jul 2010
Updated 30 Jul 2010
Type Conference
Year 2001
Where LSSC
Authors Aneta Karaivanova, Ivan Dimov, Sofiya Ivanovska
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